Eurocontrol collects the charges which are imposed by each airspace owner. They even do it for Egypt, I understand.
The charges apply to
2000kg or more, IFR.
That's why you can get a STC for the Seneca (which is just a POH change) certifying it at 1999kg.
The "biggest" touring plane you can get under 2000kg is the Jetprop - a PT6 conversion of the Piper Malibu or whatever it is called (Mirage?). The official Piper version is the Meridian which comes out at slightly over 2000kg.
Diamond probably tried to get under 2000kg with their jet but failed.
There is an argument that if too many managed to do it with airways planes, there would be a stronger case for removing the 2000kg threshold. There are people within NATS who would just like to screw everybody - some are quite open about it. If the existing route charge (by weight) formula was retained, this would massively increase the cost of flying across Europe - probably similar to a 50% rise in fuel price.
The common counter strategy is to fly VFR, often illegal VFR, which is not a good thing either. The jets are also inefficient at VFR levels, although the D-jet is an interesting case because it has been designed for lower speeds and lower levels, and could be flown VFR quite well provided the weather was OK.
The great secret of VFR flight is that it works really well so long as the pilot has an IR and can legally ask for an IFR clearance if necessary
If the charge threshold was removed, we would have a lot more of this. A 1999kg avtur burner would see a approx doubling of his fuel cost, and flying VFR at FL100 rather than IFR at FL200 would be economically well worth doing.